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Probability — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSProbability1 Mark
Question
Three digit numbers are formed using the digits 0, 2, 4, 6, 8. A number is chosen at random out of these numbers. What is the probability that this number has the same digits?
  1. $\frac{1}{16}$
  2. $\frac{16}{25}$
  3. $\frac{1}{645}$
  4. $\frac{1}{25}$
✓

Answer

The given digits are 0, 2, 4, 6, 8.

 

____ ____ ____
Hundreds Tens Ones
Now, there are 4 ways to fill the hundreds place (0 cannot occupy the hundreds place), 5 ways to fill the tens place and 5 ways to fill the ones place.

Total number of 3 digit numbers formed using the given digits = 4 × 5 × 5 = 100

The three digit numbers formed using given digits that have the same digits are 222, 444, 666 and 888

Number of 3 digit numbers that have the same digits = 4

$\therefore$ P(three digit number formed has the same digits) 

$\frac{\text{Number of 3 digits numbers that have the same digits}}{\text{Total number of 3 digit numbers formed using the given digits}}$

$=\frac{4}{100}=\frac{1}{25}$

Hence, the correct answer is option (d).

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